Is there a service which allows you to check if a paper/article was plagiarized?
At this moment, I use Google to check if some papers are plagiarized or not, but I think that are other smarter methods
There are many software options available (see Wikipedia's page on plagiarism detection), some free, and some paid.
To my knowledge, one of the most commonly used commercial options available is Turnitin; there is also Turnitin's student version, WriteCheck. Another commercial option is PlagScan. These options can be somewhat expensive though; PlagScan, for example, charges by the word: $13 gets you 50,000 words of plagiarism checking.
There are several free services, but they should be used with caution and their limitations should be understood. Some, for example, simply do what you've been doing: they take the sentences and search in Google. This "direct plagiarism" is much easier for the software to look for. Others, like the Viper plagiarism-scanner, do a pretty good job in my experience (from a long time ago), but still only match direct matches, and won't catch things where a word or two have been changed here or there. I've since stopped using them because they have a somewhat sketchy data retention and policy: whatever you upload, they add your work to their "study site" (or essay mill or whatever you want to call it). (To Viper's credit, they are transparent about how they use your data!)
If you are checking against a known local database of documents (which it doesn't sound like you're doing, but I thought I'd mention it), you can check out WCopyfind. It might not be the most intuitive, but it is promising and free. You might use this software, for example, if you have a database of papers students have submitted in the same course offered in different years, to check whether a student in the current batch of students is plagiarizing from an earlier student or from someone else in their class.